Stabilizing the output voltage is also called "regulating" the output voltage.
I suspect you have at least one of the following problems: failing power adapter, unregulated power adapter, or insufficient bypass capacitors.
Failing power adapter:
Some power adapters start to hum more and more loudly just before they fail.
You may need to replace it soon.
Are you the kind of person that:
(a) waits until a light bulb fails, then runs around in a panic trying to find a replacement? Or
(b) has a replacement light bulb in a closet so when the light bulb fails it can be replaced within minutes? Or
(c) pre-emptively replaces lightbulbs when they are near the end of their expected lifetime?
On the other hand, a few kinds of power adapters always hum relatively loudly, even when they are working perfectly.
Unregulated power adapter:
AC power in the UK and Europe is held to +-10% steady-state, and often has short-term surges and sags.
The 74LS132 datasheet only guarantees it will work with a power supply of 5 V +- 5%, so already the +- 10% change in voltage from an unregulated power adapter is out-of-spec.
Many other Schmitt trigger chips work over a much larger voltage range.
However, the power supply voltage affects the trip voltage -- so while the chip may technically may be inside spec and "work" in some sense, it may not do what you want.
The big capacitor helps smooth out short-term surges and sags, so it temporarily masked over your problem, but it does nothing for the longer-term wandering.
You need a regulated power supply, especially if you are working with audio and radio circuits. Either (a) post-regulate your unregulated power adapter with a voltage regulator such as a 7805 and some capacitors or a LM317 and some capacitors, or (b) return your unregulated power adapter, and replace it with a regulated power adapter that includes a voltage regulator built in.
Insufficient bypass capacitors:
Best practice is to attach a 1 µF capacitor to the power pins of each chip, plus a larger capacitor somewhere on the board.
(Before 2001, best practice used 0.1 µF capacitors).
Digital chips often pull brief pulses of high current, which are easily supplied by a nearby capacitor.
Without capacitors, the resistance and inductance of the long path between the chip and the voltage regulator often allows the voltage at the power pins of the chip to sag enough ("VCC droop" and "ground bounce") to reset chips with hysteresis such as Schmitt triggers and flip-flops and microcontrollers.
See question "What is a decoupling capacitor and how do I know if I need one?" for more details.